How to classify data which is spiral in shape?
There are many approaches to this kind of problem. The most obvious one is to create new features. The best features I can come up with is to transform the coordinates to spherical coordinates. 

I have not found a way to do it in playground, so I just created a few features that should help with this (sin features). After 500 iterations it will saturate and will fluctuate at 0.1 score. This suggest that no further improvement will be done and most probably I should make the hidden layer wider or add another layer.

Not a surprise that after adding just one neuron to the hidden layer you easily get 0.013 after 300 iterations. Similar thing happens by adding a new layer (0.017, but after significantly longer 500 iterations. Also no surprise as it is harder to propagate the errors). Most probably you can play with a learning rate or do an adaptive learning to make it faster, but this is not the point here.